“A game player would never prefer an outcome in which every player gets a little profit to an…

“A game player would never prefer an outcome in which
every player gets a little profit to an outcome in which he gets all the
available profit.” Is this statement true or false? Explain why in one or two
sentences.

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You and a rival are engaged in a game in which there are
three possible outcomes: you win, your rival wins (you lose), or the two of you
tie. You get a payoff of 50 if you win, a payoff of 20 if you tie, and a payoff
of 0 if you lose. What is your expected payoff in each of the following
situations?

(a) There is a 50% chance that the game ends in a tie,
but only a 10% chance that you win. (There is thus a 40% chance that you lose.)

(b) There is a 50–50 chance that you win or lose. There
are no ties.

(c) There is an 80% chance that you lose, a 10% chance
that you win, and a 10% chance that you tie.

 

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